Unsteady time-dependent incompressible Newtonian fluid flow between two parallel plates by homotopy analysis method (HAM), homotopy perturbation method (HPM) and collocation method (CM)

Analytical and numerical analyses have performed to study the problem of the flow of incompressible Newtonian fluid between two parallel plates approaching or receding from each other symmetrically. The Navier–Stokes equations have been transformed into an ordinary differential equation using a similarity transformation. The powerful analytical methods called collocation method (CM), the homotopy perturbation method (HPM), and the homotopy analysis method (HAM) have been used to solve nonlinear differential equations. It has been attempted to show the capabilities and wide-range applications of the proposed methods in comparison with a type of numerical analysis as fourth-order Runge–Kutta numerical method in solving this problem. Also, velocity fields have been computed and shown graphically for various values of physical parameters. The objective of the present work is to investigate the effect of Reynolds number and suction or injection characteristic parameter on the velocity field. Keywords: Homotopy analysis method (HAM), Collocation method (CM), Homotopy perturbation method (HPM), Parallel porous plates, Unsteady flo

Analytical approach for solving two-dimensional laminar viscous flow between slowly expanding and contracting walls

In this article, an analysis has been performed to study the two dimensional viscous flow between slowly expanding and contracting walls with weak permeability. The governing equations for the base fluid of this problem are described by dimensionless parameters wall dilation rate (α) and permeation Reynolds number (Re). The nonlinear differential equation is solved using two different analytically approaches by Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM). Then, the results are compared with numerical solution by fourth order Runge–Kutta–Fehlberg technique. Furthermore, the effects of dimensionless parameters on the velocity distributions are investigated in this research. As an important outcome, it is observed that, great agreement was found between the obtained results from the analytical and the numerical models

Heat transfer and MHD flow of non-Newtonian Maxwell fluid through a parallel plate channel : Analytical and numerical solution

Analytical and numerical analyses have been performed to study the problem of magneto-hydrodynamic (MHD) flow and heat transfer of an upper-convected Maxwell fluid in a parallel plate channel. The governing equations of continuity, momentum and energy are reduced to two ordinary differential equation forms by introducing a similarity transformation. The Homotopy Analysis Method (HAM), Homotopy Perturbation Method (HPM) and fourth-order Runge-Kutta numerical method (NUM) are used to solve this problem. Also, velocity and temperature fields have been computed and shown graphically for various values of the physical parameters. The objectives of the present work are to investigate the effect of the Deborah numbers (De), Hartman electric number (Ha), Reynolds number (Rew) and Prandtl number (Pr) on the velocity and temperature fields. As an important outcome, it is observed that increasing the Hartman number leads to a reduction in the velocity values while increasing the Deborah number has negligible impact on the velocity increment